Exam 16: A Macroscopic Description of Matter

Sometimes an experiment requires a certain pure gas to be used at reduced pressure. One way to achieve this is to purchase a sealed glass container filled with the gas, and to introduce the gas into a vacuum by attaching the glass container to the vacuum chamber and breaking the tip of the glass container using a metallic bean and a magnet. If the volume of the glass container is 1.0 L and it is at a pressure of 1.0 × 10⁵ Pa and if the vacuum chamber has a volume of 2.0 L, what will the pressure be after the gas, which is to be assumed to be an ideal gas, is released into the vacuum chamber and the temperature has returned to its original value? (Note that the glass container remains part of the system.)

2.0 L of a ideal nitrogen gas (N₂) are at 0.00°C and 1.0 atm. The ideal gas constant is R = 8.314 J/mol · K = 0.0821 L ∙ atm/mol ∙ K, Avogadro's number is 6.022 × 10²³ molecules/mol, and the ATOMIC mass of nitrogen is 14 g/mol. (a) Determine the number of moles of N₂. (b) How many molecules of N₂ are present? (c) What is the mass of this gas?

The figure shows a pV diagram for 0.95 mol of gas that undergoes the process 1 → 2. The gas then undergoes an isochoric heating from point 2 until the pressure is restored to the value it had at point 1. What is the final temperature of the gas? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.

A cold trap is set up to cause molecules to linger near the suction in a vacuum system. If the cold trap has an effective volume of 0.200 L and is maintained at 13.0 K, how many molecules are in it at 10.0 Pa of pressure? (Avogadro's number is 6.022 × 10²³ molecules/mol, and the universal gas constant is 8.314 J/mol•K. Assume the behavior of an ideal gas.)

A sealed container holds 0.020 moles of nitrogen (N₂) gas, at a pressure of 1.5 atmospheres and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. The Boltzmann constant is 1.38 × 10^-23 J/K and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K. The mass density of the gas is closest to

The number of molecules in one mole of a substance

A weather balloon contains 12.0 m³ of hydrogen gas when the balloon is released from a location at which the temperature is 22.0°C and the pressure is 101 kPa. The balloon rises to a location where the temperature is -30.0°C and the pressure is 20.0 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air.

The figure shows a pV diagram for 4.3 g of oxygen gas (O₂) in a sealed container. The temperature T₁ of the gas in state 1 is 21°C. What are the temperatures T₃ and T₄ of the gas in states 3 and 4? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the ATOMIC weight of oxygen is 16 g/mol.

3.00 moles of an ideal gas at a pressure of 250 kPa are held in a container of volume of 25.0 L. The ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K, and 1 atm = 1.01 x 10⁵ Pa. The temperature of this gas is closest to